Phase separation of self-propelled ballistic particles.

Self-propelled particles phase-separate into coexisting dense and dilute regions above a critical density. The statistical nature of their stochastic motion lends itself to various theories that predict the onset of phase separation. However, these theories are ill-equipped to describe such behavior when noise becomes negligible. To overcome this limitation, we present a predictive model that relies on two density-dependent timescales: τ_{F}, the mean time particles spend between collisions; and τ_{C}, the mean lifetime of a collision. We show that only when τ_{F}<τ_{C} do collisions last long enough to develop a growing cluster and initiate phase separation. Using both analytical calculations and active particle simulations, we measure these timescales and determine the critical density for phase separation in both two and three dimensions.